Quantum Magnetic Field Effect

A powerful new way to control X-ray emission

The quantum magnetic field effect is important in LPPF’s work, because it allows us to control how hot the electrons in the plasma are and therefore how much X-ray energy is emitted, and how much energy each X-ray photon carries. By suppressing the transfer of energy from the ions, which generate the nuclear fusion energy, to the electrons, which emit X-rays, we can reduce the amount of energy lost to the plasma by the X-rays, thus heat the plasma hotter and gain more fusion energy.

The effect only operates at extremely high fields, billions of times that of the Earth’s magnetic field, but the DPF can reach such high fields. See technical paper here.

Here is an explanation of how it works:

To understand how the magnetic effect works, it’s important to note first how ions heat electrons in the plasma. For fundamental mechanical reasons, a particle can only impart energy to particles that are traveling slower than it is. A simple way of seeing this is to imagine two runners, one fat (the ion) and one skinny (the electron). If the electron is running faster it can catch up to the ion and give it a shove, increasing the ion’s energy. But if the ion is running faster, it can give the electron a shove, increasing the skinny runner’s energy. In either case the faster particle gives up energy to the slower particle. This is the case even if the slower particle has far more energy to begin with due to its greater mass. Since ions have at least 1,836 times as much mass as electrons, slower moving ions often have far more energy than electrons, but if the electrons move faster, the ions gain still more energy at the electrons’ expense.

In plasma without a strong magnetic field, however, there are always a few electrons that are randomly moving more slowly that the ions. The ions give up energy to those electrons, which then mix in with the rest. So in “normal plasma”, energy does get equalized and the ions and electrons end up at the same temperature, with the average ion moving far slower than the average electron, but faster than some electrons.

A powerful magnetic field, more than several billion gauss (several billion times the magnetic field of the Earth) changes this situation. In any magnetic field, an electron moves in a helical orbit around the direction of the magnetic field line. The size of the orbit, the gyroradius, gets smaller for lower electron velocities and for HIGHER magnetic fields. But quantum mechanics dictates that associated with each electron is a wave, which gets longer as the electron velocity goes down. An electron can only be located with one wavelength, not within a smaller volume.

At a certain point, the gyroradius shrinks down to the same size as the electron’s wavelength. It can’t shrink any further. So, for a given magnetic field, there is a minimum velocity that an electron can have in orbiting the magnetic field line. A smaller velocity would makes its gyroradius smaller than its wavelength, which is impossible.

Because of this quantum mechanical magnetic field effect, there is a minimum momentum that must be conveyed to an electron to increase its energy. This means in turn that ions must have a certain minimum velocity to convey this momentum to the electrons.

So, instead of the ions just having to move faster than some electrons, they instead have to move faster than this minimum velocity, which depends on the magnetic field strength. If the field is strong enough, very few of the ions will have this minimum velocity, so energy transfer to the electron will be very inefficient. On the other hand, the fast electrons that can heat the ions will all have more—on average far more—than this minimum velocity, so they will heat the ions efficiently.

Because they lose energy more efficiently than they gain it, the electrons are far cooler than the ions. But since X-ray emission grows with temperature, cooler electrons lead to far less X-ray cooling. Thus by controlling the magnetic field, we can control the X-ray energy output.

The effects of magnetic fields on ion-electron collisions has been studied for some time. It was first pointed out in the 1970s by Oak Ridge researcher J. Rand McNally in a non-quantum mechanical form. More recently astronomers studying neutron stars, which have powerful magnetic fields, noted the quantum mechanical form of the effect, which is much larger. However, Lerner was the first to point out in 2003 that this quantum effect would have a large impact on the plasma focus, where such strong magnetic fields are possible. Experiments have already demonstrated 0.4 giga gauss fields, and DPFs with smaller electrodes and stronger initial magnetic fields can reach as high as 5 gigagauss, Lerner calculates. This should be achievable in the next round of LPPF’s experiments.